2078 Entrance Questions

Given, n(U)=100, n(A)= 35, n(B)= 60 and n(AUB)= 80 n(𝐴∩𝐵)=?

using formula,

n(AuB)=n(A)+n(B)-n(AnB)

or, 80=35+60-n(AnB)

or, n(AnB)=95-80

n(AnB)=15

Hence, the correct answer is option b. 15

Given,

A =[-3, 1 ] i.e {-3,-2,-1,0,1} and B =[-2, 4] i.e {-2,-1,0,1,2,3,4}

For A-B={-3,-2,-1,0,1} – {-2,-1,0,1,2,3,4} = {-3}

From option c. [-3, -2)  satisfy so

Hence, the correct answer is option c. [-3, -2)

A sentence Which is a true statement is Mount Everest is in Nepal because Mount Everest lies in Nepal which is true

Hence, the correct answer is option c. Mount Everest is in Nepal.

Given,

𝑓(𝑥) =2𝑥 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑥 𝜖𝑁.

Let x1, x2

From one to one function: f(x1)=f(x2)

f(x1)=2𝑥1,   f(x2)=2𝑥2

From the condition of one to one function

f(x1)=f(x2) so,

2𝑥1 = 2𝑥2

∴ x1=x2

Hence, the correct answer is option c. one to one

Given,

𝑓(𝑥) = 12 − 3𝑥———–(i)

For increasing: f'(x)>0 and for decreasing f'(x)<0

Differentiate equation(i) with respect to x

f'(x)=-3

So, the given function is decreasing

Hence, the correct answer is option b. decreasing

Given,

A = [-7]

the determinant of A = [-7]  is -7

Hence, the correct answer is option d. -7

Given equations are,

3𝑥 − 2𝑦 = 1———–(i)

6𝑥 −4𝑦 = 2

2(3x-2y)=2

3x-2y=1———(ii)

Here equation(i) & (ii) both are equal

Hence, the correct answer is option b. consistent and dependent

The sum of the three cube roots of one is i.e 1+𝜔^2+𝜔 =0

Hence, the correct answer is option a. 0

= Π/180 (this is the formula)

Hence, the correct answer is option c. Π/180

The correct answer is option b.

This is the De-Morgan’s  law

Hence, the correct answer is option b.

Three different digits less than 500 and the integers are 1,2,3,4,5

So, 455 but not 499 because 9 is not in the given integers so,

The numbers can be formed 4x4x3=48 ways

Hence, the correct answer is option a. 48

Given,

𝑦^2 =8𝑥 comparing with

y^2=4ax

4a=8

a=2

then, Focus(a,0)=(2,0)

Hence, the correct answer is option a. (2 ,0)

The relation between direction cosines of a line is given by 𝑙^2 + 𝑚^2 + 𝑛^2 = 1

Hence, the correct answer is option c. 𝑙^2 + 𝑚^2 + 𝑛^2 = 1

The word is “Glissando” it’s break down into syllables: glis-san-do.

Hence, the correct answer is option b. Second syllable

The word “Investigate” is stressed on the second syllable: “in-ves-ti-gate”. The other words have their stress on the first syllable.

Hence, the correct answer is option a. Investigate

“Magnitude” refers to the size or extent of something, and “gravity” can also refer to importance or seriousness,

Hence, the correct answer is option c. gravity

“Outpaced” means to move faster than or leave behind, which is synonymous with “surpassed.”

Hence, the correct answer is option d. surpassed

“Impulsive” refers to acting without thinking, while “caution” refers to careful and deliberate actions, making it an appropriate antonym.

Hence, the correct answer is option a. caution

“Reputation” refers to the general opinion held about someone, usually positive, while “notoriety” refers to being famous or well-known for negative reasons, making it the suitable opposite.

Hence, the correct answer is option c. notori

An “apostate” is someone who renounces or abandons their religious faith, belief, or principles.

Hence, the correct answer is option b. apostate

A “sinecure” is a position or job that requires little or no responsibility or work but provides a significant income.

Hence, the correct answer is option a. sinecure

The correct prepositions are “warn of” danger and “warn against” errors. “Warn of” is used to notify someone about a potential risk, and “warn against” is used to caution someone about making mistakes.

Hence, the correct answer is option b. of , against

The correct word is “Although.” The sentence would read: “Although I had that book with me, I did not give it to him.” “Although” is used to introduce a contrasting idea.

Hence, the correct answer is option c. Although

The feminine gender of “Gander” (which is a male goose) is “Goose.”

Hence, the correct answer is option d. Goose

The idiom “go through the roof” refers to something (usually prices or emotions) increasing very quickly or suddenly.

Hence, the correct answer is option a. price rise or increase quickly

“Hellenism” refers to the culture, ideals, and practices of ancient Greece.

Hence, the correct answer is option b. conformity to or imitation of ancient Greek thought customs or styles

The correct phrasal verb is “set on.” The sentence would read: “When he was passing through the door, the dogs suddenly set on him. “Set on” means to attack someone suddenly.

Hence, the correct answer is option c. set on

“Clear up” means to tidy or clean something. The correct sentence is: “Would you like to help me clear up the writing desk?”

Hence, the correct answer is option a. Clear up

“A stick in the mud” refers to someone who is resistant to change, stuck in old ways, and not open to new ideas or innovations.

Hence, the correct answer is option d. A person with fixed views and ideas and not ready for any changes

“Otherwise” is the correct choice. The sentence would read: “We must be early; otherwise, we won’t get seats.” It indicates that not being early will result in not getting seats.

Hence, the correct answer  is option a. otherwise

“While” is used to show contrast between two situations happening at the same time. The correct sentence is: “Some people waste food while others haven’t enough.”

Hence, the correct answer is option b. While

“The” is the correct article here. The sentence should read: “If you interfere with the nature, you will suffer for it.” “The” is used to refer to nature as a specific concept or entity.

Hence, the correct answer is option a. the

This is a tag question. The sentence “Someone had recognized him” is positive, so the tag should be negative: “hadn’t they?” “They” is used as a gender-neutral singular pronoun here.

Hence, the correct answer is option a. hadn’t they

“Resemblance” is the correct word because it means similarity or likeness. The sentence means that the photographs did not look like the original at all.

Hence, the correct answer is option b. resemblance

“Respectable” refers to something that is decent or proper, and in this context, it means they wear clothes that are appropriate and decent, even if they are not rich.

Hence, the correct answer is option c. respectable

“Site” is the correct answer because it refers to a location or place where something is constructed or set up. “This is the site chosen for the school complex.”

Hence, the correct answer is option d. sight

“Honorary” refers to a position or work for which no salary is paid. It’s often a role given as an honor without financial compensation.

Hence, the correct answer is option b. honorary

To find the dimensional formula of $c$, we start by recognizing that $v$ (velocity) has the dimensional formula [LT^−1].

The term ct^2 must have the same dimensions as velocity, so:

[c][T^2]=[LT^−1]

[c]= [LT^−1] / [T^2]

[c]=[𝑀^0 𝐿 𝑇^-3 ]

Hence, the correct answer is option d. [𝑀^0 𝐿 𝑇^-3 ]

Given magnitudes of two vectors ∣A∣=3| , ∣B∣=4, and scalar product (A⋅B)=6:

The scalar product (dot product) of two vectors $\mathbf{A}$ and $\mathbf{B}$ is given by:

A⋅B=∣A∣∣B∣cosθ

then, 6=3×4×cosθ

cosθ=6/12 = 1/2

cosθ=1/2​ corresponds to θ=60°

Hence, the correct answer is option c. 60°

The apparent motion of stars from east to west is due to the rotation of the Earth from west to east. This creates the illusion that the stars are moving in the opposite direction.

Hence, the correct answer is option b. the earth rotates from west to east.

On ice, friction is significantly reduced. Taking smaller steps helps in maintaining balance by ensuring that the force you apply while walking is within the limits of the available friction, thereby reducing the risk of slipping.

Hence, the correct answer is option b. smaller friction

Given,

Mass(m)=120 kg

Time(t)=10 sec

velocity(v)=108 km/hr = (108 x1000) / 3600  m/s= 30m/s

using Newton’s second law,

F=(m×Δv)/ Δt = 120×(0−30) /10 = -3600/10 = -360N

The negative sign indicates that the force is applied in the opposite direction of motion to stop the scooter. The magnitude of the force is 360 N.

Hence, the correct answer is option a. 360N​

Given,

$\text{ m}$, L=2m, λ=589×10^−9 m, and $0$.

To find the slit separation d, we use the formula for the position of the $n$-th bright fringe:

yn​=nλL/d

0.0344=(10×589×10^−9×2​)/d

d=​(10×589×10^−9×2​)/0.0344=0.24 mm

Hence, the correct answer is option a. 0.24mm

Upthrust (buoyant force) is given by Archimedes’ principle, which states that the upthrust is equal to the weight of the liquid displaced by the submerged part of the body. This depends on the volume of the liquid displaced, not on the shape, depth, or mass of the body itself.

Hence, the correct answer is option c. volume of liquid displaced

The thermal expansion in length depends only on the initial length, the material’s coefficient of linear expansion, and the temperature change. Since both rods are of the same material and length and are subjected to the same temperature change, the increase in length will be the same for both rods, regardless of their diameters.

Hence, the correct answer is option c. Same in both rods

The mean free path λ is inversely proportional to the pressure of the gas. As pressure increases, the number of collisions increases, reducing the mean free path. Hence, λ∝1/P.

Hence, the correct answer is option b. P^−1

The boiling point of water increases with pressure. Inside a pressure cooker, the pressure is higher than atmospheric pressure, so water boils at a temperature higher than $100°C$. Typically, it boils around 120°C under the increased pressure.

Hence, the correct answer is option c. 120°C

When a ray of light passes through a rectangular glass slab, it undergoes refraction twice: once when it enters the glass slab from air, and again when it exits the glass slab back into air.

At the first boundary (air to glass): The ray bends towards the normal because glass is denser than air.

Inside the slab: The ray travels straight because the sides of the glass slab are parallel. The light ray inside the slab is parallel to the original incident ray but displaced.

At the second boundary (glass to air): The ray bends away from the normal as it exits the denser medium (glass) to the less dense medium (air).

In option B, the ray emerges from the slab parallel to the incident ray but shifted, which correctly represents the behavior of light through a glass slab.

Hence, the correct answer is option b

Far-sightedness, or hyperopia, occurs when the eye is too short or the cornea has too little curvature. As a result, light from distant objects focuses behind the retina instead of directly on it, causing distant objects to appear blurry.

Hence, the correct answer is option b. behind the retina

A charge in uniform motion generates both an electric field and a magnetic field. The moving charge creates a magnetic field perpendicular to its direction of motion, and the charge itself also maintains an electric field.

Hence, the correct answer is option c. both electric and magnetic field

To increase the capacitance of a parallel plate capacitor, a dielectric material (such as mica) should be introduced between the plates. Dielectrics increase the capacitance by reducing the electric field within the capacitor, allowing it to store more charge for a given voltage.

Hence, the correct answer is option d. mica

Given,

Self-inductance of the coil(L)= 5mH = 5×10^−3

Current(I)=2

The magnetic flux(Φ) through a coil is given by the formula:

Φ=L×I

Φ=5×10^−3 x 2 = 0.01×10^−3=0.001 weber

Hence, the correct answer is option d. $\text{0.001 weber}$.

Given,

Power(P)=100W

Voltage(V)=220V

Power(P1)=440V

The power consumed by a bulb is given by P=V^2/R where V is the voltage and R is the resistance.

First, let’s calculate the resistance of the bulb:

R=V^2/P​=220^2/100=484Ω

Now, using this resistance at 440V:

P′=V^2/R = 440^2 / 484 = 400W

Hence, the correct answer is option d. 400W

The electric field intensity at the surface of a charged conductor is directed normally (perpendicular) to the surface. This is because the charges on a conductor in electrostatic equilibrium reside on the surface and distribute themselves in such a way that the electric field inside the conductor is zero, and the field outside the surface is perpendicular to the surface.

Hence, the correct answer is option d. directed normally to the surface

In an RLC circuit, for frequencies higher than the resonant frequency, the inductive reactance (XL​) dominates over the capacitive reactance (XC). Thus, the circuit behaves inductively at these higher frequencies.

Hence, the correct answer is option c. inductive

A material used for permanent magnets should have:

High retentivity: To retain a significant amount of magnetism after the external magnetizing field is removed.

High coercivity: To resist demagnetization by external magnetic fields or other influences.

Hence, the correct answer is option d. high retentivity, high coercivity

The angle of dip, also known as magnetic inclination, is the angle between the direction of the Earth’s magnetic field and the horizontal plane. It indicates how steeply the magnetic field lines enter or exit the Earth’s surface.

Hence, the correct answer is option c. between Earth’s magnetic field’s direction and horizontal direction

When an electron is subjected to an electric field, the force on the electron is in the direction of the electric field. If the electron has an initial velocity perpendicular to the electric field, it will experience a force in the direction of the field, causing it to accelerate along that direction. As a result, the electron’s trajectory will be parabolic, similar to the motion of a projectile under gravity.

Hence, the correct answer is option b. parabola

The Planck’s constant $h$ is experimentally determined through the photoelectric effect experiment. When light of different frequencies shines on a metal surface, electrons are ejected, and the kinetic energy of these electrons can be measured. The relationship between the energy of the photons (determined by their frequency) and the kinetic energy of the ejected electrons is given by Einstein’s photoelectric equation, which involves Planck’s constant.

Hence, the correct answer is option d. photo-electric experiment.

Given,

Pheat​=600W

Accelerating voltage (V)=50 kV=50×10^3 V

The power $P$ converted to heat can be given as:

Pheat​=(100%−0.4%)×Ptotal​ =99.6%×Ptotal

Total power Ptotal=Pheat/0.996

Ptotal​=600/0.996​≈602.41W

Now, use Ptotal=V×I

I=(602.41W)/(50×10^3V)​≈0.012A

Hence, the correct answer is option b. 0.012 A

Hence, the correct answer is option c

In the depletion region of a p-n junction diode, the mobile charge carriers (electrons and holes) are depleted, leaving behind only the fixed, immobile ions. These ions are the ionized donor atoms on the n-side and the ionized acceptor atoms on the p-side, which create the electric field across the depletion layer. This region has very few free electrons or holes, and thus it is called the “depletion” region.

Hence, the correct answer is option d. only fixed ions

Given,

The molar mass of O₂ (oxygen gas) is 32 g/mol (16 g/mol per oxygen atom times 2).

One mole of O₂ contains Avogadro’s number of molecules, which is 6.02 × 10^23.

So, 32 grams of O₂ is exactly 1 mole of O₂, which contains 6.02 × 10^23 molecules.

Hence, the correct answer is option b. 6.02 × 10^23

Pauli’s exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers. This principle is fundamental to quantum mechanics and electron configuration in atoms

Hence, the correct answer is option a. Pauli’s exclusion principle

Sulfur hexafluoride (SF₆) has six bonding pairs around the central sulfur atom and no lone pairs. According to VSEPR (Valence Shell Electron Pair Repulsion) theory, this arrangement leads to an octahedral shape.

Hence, the correct answer is option c. octahedral

Protium, deuterium, and tritium are all isotopes of hydrogen. Fullerene, however, is a molecule composed of carbon atoms, not an isotope of hydrogen.

Hence, the correct answer is option d. fullerene

The brown ring test is used to detect the presence of nitrate ions (NO₃⁻). The brown ring is formed by the reaction of nitrate ions with iron(II) sulfate (FeSO₄) in the presence of concentrated sulfuric acid (H₂SO₄), forming a complex of FeSO₄ with nitric oxide (NO).

Hence, the correct answer is option a. FeSO₄·NO

“Hyposulphite” or “hypo” commonly refers to sodium thiosulphate (Na₂S₂O₃). In this case, the given options seem to refer to different compounds, but the closest to the formula for hypo is H₂S₂O₃, which is also known as thiosulfurous acid. However, this option is not the exact formula for hypo, which is more accurately Na₂S₂O₃. None of the given options directly match sodium thiosulphate, but H₂S₂O₃ is related to the compound’s chemical family.

Hence, the correct answer is option a. H₂S₂O₃

Magnesium sulfate heptahydrate (MgSO₄·7H₂O) is commonly known as Epsom salt.

Hence, the correct answer is option c. epsom salt

Minamata disease is a neurological syndrome caused by mercury poisoning. It was first identified in Minamata Bay, Japan, where industrial discharge of mercury contaminated the local fish.

Hence, the correct answer is option d. mercury

Lassaigne’s test is used to detect the presence of nitrogen, sulfur, and halogens (chlorine, bromine, iodine) in organic compounds. Fluorine cannot be detected using Lassaigne’s test because it does not form a soluble complex with sodium fusion.

Hence, the correct answer is option a. Fluorine

To distinguish between alkyne and alkane, ammoniac silver nitrate (also known as Tollens’ reagent) is used. Alkynes react with this reagent to form a precipitate of silver, whereas alkanes do not react.

Hence, the correct answer is option b. Ammoniac silver nitrate

The Friedel-Crafts alkylation reaction involves the introduction of an alkyl group into an aromatic ring. This reaction requires a Lewis acid catalyst to facilitate the formation of the carbocation intermediate. The most commonly used catalyst for Friedel-Crafts alkylation is anhydrous AlCl₃ (aluminum chloride).

Hence, the correct answer is option c. Anhydrous AlCl₃

Urea is a nitrogenous fertilizer, as it contains a high percentage of nitrogen, which is essential for plant growth. It is commonly used to supply nitrogen to crops.

Hence, the correct answer is option a. Nitrogenous fertilizer

Acetone is a common name for the compound with the IUPAC name propanone. It is the simplest ketone and consists of a three-carbon chain with a carbonyl group.

Hence, the correct answer is option c. Propanone

The equivalent weight of sulfuric acid (H₂SO₄) is calculated based on its ability to donate protons (H⁺ ions) in reactions. Sulfuric acid is a diprotic acid (can donate two protons). Therefore, its equivalent weight is its molar weight divided by the number of replaceable hydrogen ions (2).

Hence, the correct answer is option d. mol. wt./2

The rate of reaction is generally dependent on the concentration of reactants, temperature, and particle size (which affects the surface area). Molecularity refers to the number of reacting species in an elementary reaction step and is not directly related to the rate of the overall reaction in the way concentration and temperature are.

Hence, the correct answer is option a. molecularity

The statement “The total amount of energy in the universe remains constant” refers to the principle that energy cannot be created or destroyed, only transformed from one form to another. This principle is encapsulated by the first law of thermodynamics, also known as the law of energy conservation.

Hence, the correct answer  is option b. first law

Organophosphate insecticides are a class of chemicals that inhibit the enzyme acetylcholinesterase, leading to the accumulation of acetylcholine and resulting in pest control. Malathion is a well-known organophosphate insecticide. DDT, BHC, and dieldrin are not organophosphates; they belong to different classes of insecticides.

Hence, the correct answer is option c. Malathion

Aniline (C₆H₅NH₂) is a typical aromatic amine and is known for its ability to undergo coupling reactions, such as the formation of azo dyes with diazonium salts. Aniline does react with aldehydes to form Schiff bases. Thus, option d. “Does not give coupling reaction” is not true, because aniline does participate in coupling reactions.

Hence, the correct answer is option d. does not give coupling reaction

Ethyl alcohol with 100 percent purity is known as absolute alcohol. Rectified spirit is alcohol with high purity but not necessarily 100 percent, and denatured alcohol has additives to make it undrinkable.

Hence, the correct answer is option a. absolute alcohol

The reaction in which haloalkanes (alkyl halides) are heated with sodium metal in the presence of ether to form alkanes is known as the Wurtz reaction.

Hence, the correct answer is option b. Wurtz reaction

Ketones generally do not react with Tollen’s reagent or Fehling’s solution. These reagents are used to test for aldehydes, which can reduce them. Ketones do not reduce these reagents, thus they are not oxidized by them. Similarly, ketones do not react with Benedict’s solution for the same reason

Hence, the correct answer is option c. reduce Tollen’s reagent

CO₂ (carbon dioxide) acts as a Lewis acid because it can accept a pair of electrons. In the context of acid-base chemistry, it reacts with water to form carbonic acid (H₂CO₃), demonstrating its acidic properties. However, it’s primarily recognized as a Lewis acid due to its electron-pair accepting nature.

Hence, the correct answer is option d. Lewis acid

Galvanizing is the process of coating iron or steel with a layer of zinc to prevent rusting. Zinc is commonly used for this purpose due to its protective properties.

hence, the correct answer is option a. zinc

“Lunar caustic” is the name historically given to silver nitrate (AgNO₃). It was used in early times for various purposes, including medical applications.

Hence, the correct answer is option b. AgNO₃

The strength of an acid is influenced by the stability of its conjugate base. The more electron-withdrawing groups attached to the carboxyl group, the stronger the acid. Among the given compounds, trichloroacetic acid (Cl₃CCOOH) is the strongest acid because the three chlorine atoms strongly withdraw electron density through inductive effects, stabilizing the conjugate base.

Hence, the correct answer is option c. Cl₃CCOOH